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8.3 Scale Diagrams
Scale diagrams can be used to represent 2­dimensional
shapes.
To create a scale diagram, you must determine an appropriate
scale to use. This is called the scale factor. It depends on the
dimensions of the original shape and the size of diagram that is
required.
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The scale factor represents the ratio of a distance measurement of a
shape to the corresponding distance measurement of a similar
shape. Both measurements are expressed using the same units.
Click the icon for a YouTube Video on Scale Diagrams
in Math and Unit Conversions
Click the icon for a GREAT movie on Scale Factor
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Determining Scale Factor
An easy way to determine the scale factor, k, used in a scale diagram,
we use the following guideline.
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How Does Scale Factor Affect the Original Shape
When a scale factor is between 0 and 1, the new shape is a reduction
of the original shape.
When a scale factor is greater than 1, the new shape is an
enlargement of the original shape.
Click the icon for a YouTube Video on Reductions and
Enlargements
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Example
The Garry oak is a tree that is found on Vancouver Island. The original acorn
for these scale diagrams was 1.9 cm long. Determine the scale factor that was
used for each diagram.
Possible
Solution:
a. length of acorn = 2.3 cm
The scale factor is 1.2.
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Example
This top view of a hex­nut must be enlarged by a
scale factor of 250% for a display at a trade
show.
a) Measure the necessary distances on the
diagram.
b) Determine what the corresponding distances
on the enlarged diagram should be.
c) Draw the scale diagram of the hex­nut.
Possible
Solution:
a) I made the following measurements: innermost diameter = 1.6 cm middle inner diameter = 2.5 cm outer diameter = 3.4 cm hexagon side = 2.0 cm b) The scale factor is 2.5. new innermost diameter = 2.5(1.6 cm) new innermost diameter = 4.0 cm new middle inner diameter = 2.5(2.5 cm) new middle inner diameter = 6.25 cm new outer diameter = 2.5(3.4 cm) new outer diameter = 8.5 cm new hexagon side = 2.5(2.0 cm) new hexagon side = 5.0 cm
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Example
A billboard measures 4.5 m by 3.5 m. Draw a scale diagram of the
billboard that fits in a space measuring 20 cm by 15 cm.
Solution:
e.g., The scale diagram of the billboard could be a rectangle
measuring 18 cm by 14 cm.
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